# College Algebra 1e

### Chapter R: Review of Prerequisites

#### Section R.1 Sets and the Real Number Line

#### Section R.2 Models, Algebraic Expressions, and Properties of Real Numbers

#### Section R.3 Integer Exponents and Scientific Notation

#### Section R.4 Rational Exponents and Radicals

#### Section R.5 Polynomials and Multiplication of Radicals

Problem Recognition Exercises: Simplifying Algebraic Expressions

#### Section R.6 Factoring

#### Section R.7 Rational Expressions and More Operations on Radicals

### Chapter 1: Equations and Inequalities

#### Section 1.1 Linear Equations and Rational Equations

#### Section 1.2 Applications and Modeling with Linear Equations

#### Section 1.3 Complex Numbers

#### Section 1.4 Quadratic Equations

Problem Recognition Exercises: Simplifying Expressions versus Solving Equations

#### Section 1.5 Applications of Quadratic Equations

#### Section 1.6 More Equations and Applications

#### Section 1.7 Linear Inequalities and Compound Inequalities

#### Section 1.8 Absolute Value Equations and Inequalities

Problem Recognition Exercises: Recognizing and Solving Equations and Inequalities

### Chapter 2: Functions and Graphs

#### Section 2.1 The Rectangular Coordinate System and Graphing Utilities

#### Section 2.2 Circles

#### Section 2.3 Functions and Relations

#### Section 2.4 Linear Equations in Two Variables and Linear Functions

#### Section 2.5 Applications of Linear Equations and Modeling

Problem Recognition Exercises: Comparing Graphs of Equations

#### Section 2.6 Transformation of Graphs

#### Section 2.7 Analyzing Graphs of Functions and Piecewise-Defined Functions

#### Section 2.8 The Algebra of Functions

### Chapter 3: Polynomial and Rational Functions

#### Section 3.1 Quadratic Functions and Applications

#### Section 3.2 Introduction to Polynomial Functions

#### Section 3.3 Division of Polynomials and the Remainder and Factor Theorems

#### Section 3.4 Zeros of Polynomials

#### Section 3.5 Rational Functions

Problem Recognition Exercises: Polynomial and Rational Functions

#### Section 3.6 Polynomial and Rational Inequalities

Problem Recognition Exercises: Solving Equations and Inequalities

#### Section 3.7 Variation

### Chapter 4: Exponential and Logarithmic Functions

#### Section 4.1 Inverse Functions

#### Section 4.2 Exponential Functions

#### Section 4.3 Logarithmic Functions

Problem Recognition Exercises: Analyzing Functions

#### Section 4.4 Properties of Logarithms

#### Section 4.5 Exponential and Logarithmic Equations

#### Section 4.6 Modeling with Exponential and Logarithmic Functions

### Chapter 5: Systems of Equations and Inequalities

#### Section 5.1 Systems of Linear Equations in Two Variables and Applications

#### Section 5.2 Systems of Linear Equations in Three Variables and Applications

#### Section 5.3 Partial Fraction Decomposition

#### Section 5.4 Systems of Nonlinear Equations in Two Variables

#### Section 5.5 Inequalities and Systems of Inequalities in Two Variables

Problem Recognition Exercises: Equations and Inequalities in Two Variables

#### Section 5.6 Linear Programming

### Chapter 6: Matrices and Determinants and Applications

#### Section 6.1 Solving Systems of Linear Equations Using Matrices

#### Section 6.2 Inconsistent Systems and Dependent Equations

#### Section 6.3 Operations on Matrices

#### Section 6.4 Inverse Matrices and Matrix Equations

#### Section 6.5 Determinants and Cramer’s Rule

Problem Recognition Exercises: Using Multiple Methods to Solve Systems of Linear Equations

### Chapter 7: Analytic Geometry

#### Section 7.1 The Ellipse

#### Section 7.2 The Hyperbola

#### Section 7.3 The Parabola

Problem Recognition Exercises: Comparing Equations of Conic Sections and Investigating the General Equation

### Chapter 8: Sequences, Series, Induction, and Probability

#### Section 8.1 Sequences and Series

#### Section 8.2 Arithmetic Sequences and Series

#### Section 8.3 Geometric Sequences and Series

Problem Recognition Exercises: Comparing Arithmetic and geometric Sequences and Series